#color(red)("How you would normally see the calculation")#
variants on:
#color(red)(-(2xx5)(a^(7-2)) = -10a^5)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(green)("Very detailed solution split into 3 parts")#
Part 1 #-># signs
Part 2 #-># numbers
Part 3 #-># the letters (variables)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Part 1 "-> " signs")#
Write the signs as -1 and +1#" "# ( this does work!)
The signs are not the same as each other so
#(-1)xx(+1) = color(red)((-1))#
#color(blue)("So our answer is a negative value ")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Part 2 "-> " numbers")#
#2xx5 =color(red)(10)#
#color(blue)("The number part of the answer is 10")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Part 3 "-> " letters (variables)")#
We have:#" "a^7xxa^(-2)#
#color(brown)("Shortcut method")#
Because the letters (variables) are the same we can do this:
#a^7xxa^(-2)" "=" "a^(7-2)" "=color(red)(a^5)#
'......................................................
#color(brown)("First principles method")#
#a^(-2)" is the same thing as "1/a^2#
So::#" "a^7xxa^(-2)" " =" " a^7xx1/a^2#
Let #a^7# be written as #a^5xxa^2#
Then we have: #a^5xxa^2xx1/a^2#
This is the same as
#" "a^5xxa^2/a^2#
But #a^2/a^2=1#
#" "a^5xxa^2/a^2" "=" "color(red)(a^5)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("putting it all together")#
#color(red)((-2a^7)(5a^(-2))= -10a^5)#
